Skip to main content

Modeling Dynamic Preferences: A Bayesian Robust Dynamic Latent Ordered Probit Model

  • Daniel Stegmueller (a1)

Much politico-economic research on individuals' preferences is cross-sectional and does not model dynamic aspects of preference or attitude formation. I present a Bayesian dynamic panel model, which facilitates the analysis of repeated preferences using individual-level panel data. My model deals with three problems. First, I explicitly include feedback from previous preferences taking into account that available survey measures of preferences are categorical. Second, I model individuals' initial conditions when entering the panel as resulting from observed and unobserved individual attributes. Third, I capture unobserved individual preference heterogeneity both via standard parametric random effects and a robust alternative based on Bayesian nonparametric density estimation. I use this model to analyze the impact of income and wealth on preferences for government intervention using the British Household Panel Study from 1991 to 2007.

Hide All
Aitkin, Murray. 1999. A general maximum likelihood analysis of variance components in generalized linear models. Biometrics 55: 117–28.
Akay, Alpaslan. 2012. Finite-sample comparison of alternative methods for estimating dynamic panel data models. Journal of Applied Econometrics 27: 1189–204.
Albert, James H., and Chib, Siddhartha. 1993. Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association 88: 669–79.
Albert, Jim, and Chib, Siddhartha. 1995. Bayesian residual analysis for binary response regression models. Biometrika 82: 747–59.
Alesina, Alberto, and Ferrara, Eliana La. 2005. Preferences for redistribution in the land of opportunities. Journal of Public Economics 89: 897931.
Alesina, Alberto, and Angeletos, George-Marios. 2005. Fairness and redistribution. American Economic Review 95: 960–80.
Alesina, Alberto, and Giuliano, Paola. 2011. Preferences for redistribution. In Handbook of social economics, eds. Benhabib, Jess, Bisin, Alberto, and Jackson, Matthew O., 93131. San Diego, CA: North-Holland.
Anderson, T. W., and Hsiao, C. 1981. Estimation of dynamic models with error components. Journal of the American Statistical Association 76: 598606.
Antoniak, Charles E. 1974. Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Annals of Statistics 2: 1152–74.
Arellano, Manuel, and Bond, Stephen. 1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58: 277.
Arellano, Manuel, and Carrasco, Raquel. 2003. Binary choice panel data models with predetermined variables. Journal of Econometrics 115: 125–57.
Arulampalam, Wiji. 2000. Unemployment persistence. Oxford Economic Papers 52: 2450.
Arulampalam, Wiji, and Stewart, Mark B. 2009. Simplified implementation of the Heckman estimator of the dynamic probit model and a comparison with alternative estimators. Oxford Bulletin of Economics and Statistics 71: 659–81.
Bartels, Brandon L., Box-Steffensmeier, Janet M., Smidt, Corwin D., and Smith, Rene M. 2011. The dynamic properties of individual-level party identification in the United States. Electoral Studies 30: 210–22.
Beck, Nathaniel, and Katz, Jonathan N. 1996. Nuisance vs. substance: Specifying and estimating time-series-cross-section models. Political Analysis 6: 136.
Blundell, Richard, and Bond, Stephen. 1998. Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87: 115–43.
Brooks, Stephen P., and Roberts, Gareth O. 1998. Convergence assessment techniques for Markov chain Monte Carlo. Statistics and Computing 8: 319–35.
Cusack, Thomas, Iversen, Torbern, and Rehm, Phillip. 2005. Risks at work: The demand and supply sides of government redistribution. Oxford Review of Economic Policy 22: 365–89.
Cusack, Thomas, Iversen, Torbern, and Rehm, Phillip. 2008. Economic shocks, inequality, and popular support for redistribution. In Democracy, inequality, and representation: A comparative perspective, eds. Beramendi, Pablo and Anderson, Christopher J., 203–31. New York: Russell Sage Foundation.
Czado, Claudia, Heyn, Anette, and Müller, Gernot. 2011. Modeling individual migraine severity with autoregressive ordered probit models. Statistical Methods and Application 20: 101–21.
Dunson, David B., Pillai, Natesh, and Park, Ju-Hyun. 2007. Bayesian density regression. Journal of the Royal Statistical Society B 69: 163–83.
Eckstein, Zvi, and Wolpin, Kenneth. 1999. Why youths drop out of high school: The impact of preferences, opportunities, and abilities. Econometrica 67: 1295–339.
Escobar, Michael D. 1995. Nonparametric Bayesian methods in hierarchical models. Journal of Statistical Planning and Inference 43: 97106.
Escobar, Michael D., and West, Mike. 1998. Computing Bayesian nonparametric hierarchical models. In Practical nonparametric and semiparametric Bayesian statistics, eds. Dey, Dipak K., Müller, Peter, and Sinha, Debajyoti, 122. Springer.
Ferguson, Thomas S. 1973. A Bayesian analysis of some nonparametric problems. Annals of Statistics 1: 209–30.
Ferguson, Thomas S. 1974. Prior distributions on spaces of probability measures. Annals of Statistics 2: 615–29.
Follmann, Dean A., and Lambert, Diane. 1989. Generalizing logistic regression by nonparametric mixing. Journal of the American Statistical Association 84: 295300.
Fotouhi, Ali Reza. 2005. The initial conditions problem in longitudinal binary process: A simulation study. Simulation Modelling Practice and Theory 13: 566–83.
Franses, Philip Hans, and Cramer, J. S. 2010. On the number of categories in an ordered regression model. Statistica Neerlandica 64: 125–8.
Friedman, M. 1957. A Theory of the Consumption Function. Princeton, NJ: Princeton University Press.
Gelman, Andrew. 2006. Prior distributions for variance parameters in hierarchical models. Bayesian Analysis 1: 515–34.
Gelman, Andrew. 2008. Scaling regression inputs by dividing by two standard deviations. Statistics in Medicine 27: 2865–73.
Gelman, Andrew, Carlin, John B., Stern, Hal S., and Rubin, Donald B. 2004. Bayesian Data Analysis. Boca Raton, FL: Chapman & Hall.
Gelman, Andrew, and Rubin, Donald. 1992. Inference from iterative simulation using multiple sequences. Statistical Science 7: 457511.
Ghosh, J. K., and Ramamoorthi, R. V. 2003. Bayesian nonparametrics. New York: Springer.
Gill, Jeff. 2008a. Bayesian methods: A social and behavioral sciences approach. Boca Raton, FL: Chapman & Hall.
Gill, Jeff. 2008b. Is partial-dimension convergence a problem for inferences from MCMC algorithms? Political Analysis 16: 153–78.
Gill, Jeff, and Casella, George. 2009. Nonparametric priors for ordinal Bayesian social science models: Specification and estimation. Journal of the American Statistical Association 104: 112.
Greene, William, and Hensher, David. 2010. Modeling ordered choices: A primer. Cambridge, UK: Cambridge University Press.
Grimmer, Justin. 2010. An introduction to Bayesian inference via variational approximations. Political Analysis 19: 3247.
Hagenaars, A., de Vos, K., and Zaidi, M. A. 1994. Poverty statistics in the late 1980s: Research based on micro-data. Luxembourg: Office for Official Publications of the European Communities.
Hanson, Timothy E., Branscum, Adam J., and Johnson, Wesley O. 2005. Bayesian nonparametric modeling and data analysis: An introduction. In Handbook of statistics, Vol. 25, 245–78. Amsterdam: Elsevier.
Harris, Mark N., Matyas, Laszlo, and Sevestre, Patrick. 2008. Dynamic models for short panels. In The econometrics of panel data: Fundamentals and recent developments in theory and practice, eds. Matyas, Laszlo and Sevestre, Patrick, 249–78. Berlin, Germany: Springer.
Hasegawa, Hikaru. 2009. Bayesian dynamic panel-ordered probit model and its application to subjective well-being. Communications in Statistics: Simulation and Computation 38: 1321–47.
Heckman, James J. 1978. Dummy endogeneous variables in a simultaneous equation system. Econometrica 46: 931–59.
Heckman, James J. 1981a. Heterogeneity and state dependence. In Studies in labor markets, ed. Rosen, Sherwin, 91140. Chicago: University of Chicago Press.
Heckman, James J. 1981b. The incidental parameters problem and the problem of initial conditions in estimating a discrete time-discrete data stochastic process. In Structural analysis of discrete data with econometric applications, eds. Manski, C. F. and McFadden, Daniel, 179–95. Cambridge, MA: MIT Press.
Heckman, James J., and Singer, B. 1984. A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica 52: 271320.
Imai, Kosuke, Lu, Ying, and Strauss, Aaron. 2008. Bayesian and likelihood inference for 2 x 2 ecological tables: An incomplete-data approach. Political Analysis 16: 4169.
Iversen, Torben, and Soskice, David. 2001. An asset theory of social policy preferences. American Political Science Review 95: 875–93.
Jackman, Simon. 2000. Estimation and inference are missing data problems: Unifying social science statistics via Bayesian simulation. Political Analysis 8: 307–32.
Jackman, Simon. 2009. Bayesian analysis for the social sciences. New York: Wiley.
Jackman, Simon, and Western, Bruce. 1994. Bayesian inference for comparative research. American Political Science Review 88: 412–23.
Jara, Alejandro, Jose Garcia-Zattera, Maria, and Lesaffre, Emmanuel. 2007. A Dirichlet process mixture model for the analysis of correlated binary responses. Computational Statistics and Data Analysis 51: 5402–15.
Johnson, Valen E., and Albert, Jim H. 1999. Ordinal data modeling. New York: Springer.
Keane, M. P. 1997. Modeling heterogeneity and state dependence in consumer choice behavior. Journal of Business & Economic Statistics 15: 310–27.
Kleinman, Ken P., and Ibrahim, Joseph G. 1998. A semiparametric Bayesian approach to the random effects model. Biometrics 54: 921–38.
Kottas, Athanasios, Müller, Peter, and Quintana, Fernando. 2005. Nonparametric Bayesian modeling for multivariate ordinal data. Journal of Computational and Graphical Statistics 14: 610–25.
Kyung, Minyung, Gill, Jeff, and Casella, George. 2010. Estimation in Dirichlet random effects models. Annals of Statistics 38: 9791009.
Laird, N. 1978. Nonparametric maximum likelihood estimation of a mixture distribution. Journal of the American Statistical Association 73: 805–11.
Lange, Kenneth L., Little, Roderick J. A., and Taylor, Jeremy M. G. 1989. Robust statistical modeling using the t-distribution. Journal of the American Statistical Association 84: 881–96.
Lindsay, Bruce. 1995. Mixture models: Theory, geometry and applications. Hayward, CA: Institute of Mathematical Statistics.
Lunn, David J., Wakefield, Jon, and Racine-Poon, Amy. 2001. Cumulative logit models for ordinal data: A case study involving allergic rhinitis severity scores. Statistics in Medicine 20: 2261–85.
Margalit, Yotam. 2013. Explaining social policy preferences: Evidence from the great recession. American Political Science Review 107: 80103.
McKelvey, Richard D., and Zavoina, William. 1975. A statistical model for the analysis of ordinal level dependent variables. Journal of Mathematical Sociology 4: 103–20.
Moene, Kark Ove, and Wallerstein, Michael. 2001. Inequality, social insurance, and redistribution. American Political Science Review 95: 859–74.
Müller, Gernot, and Czado, Claudia. 2005. An autoregressive ordered probit model with application to high-frequency financial data. Journal of Computational and Graphical Statistics 14: 320–38.
Müller, Peter, and Quintana, Fernando. 2004. Nonparametric Bayesian data analysis. Statistical Science 19: 95110.
Müller, Peter, Quintana, Fernando, and Rosner, Gary L. 2007. Semiparametric Bayesian inference for multilevel repeated measurement data. Biometrics 63: 280–89.
Mundlak, Yair. 1978. On the pooling of time-series and cross-section data. Econometrica 46: 6985.
Navarro, Daniel J., Griffiths, Thomas L., Steyvers, Mark, and Lee, Michael D. 2006. Modeling individual differences using Dirichlet processes. Journal of Mathematical Psychology 50: 101–22.
Nerlove, Marc, Sevestre, Patrick, and Balestra, Pietro. 2008. Introduction. In The econometrics of panel data: Fundamentals and recent developments in theory and practice, eds. Matyas, Laszlo and Sevestre, Patrick, 322. Berlin: Springer.
Neustadt, Ilja. 2010. Do religious beliefs explain preferences for income redistribution? Experimental evidence. University of Zurich, Socioeconomic Institute working paper 1009.
Nickell, Stephen. 1981. Biases in dynamic models with fixed effects. Econometrica 49: 1417–26.
Pang, Xun. 2010. Modeling heterogeneity and serial correlation in binary time-series cross-sectional data: A Bayesian multilevel model with AR(p) errors. Political Analysis 18: 470–98.
Pudney, Stephen. 2006. The dynamics of perception: Modelling subjective well-being in a short panel. ISER working paper 2006–27.
Pudney, Stephen. 2008. The dynamics of perception: Modelling subjective well-being in a short panel. Journal of the Royal Statistical Society A 171: 2140.
Rabe-Hesketh, Sophia, and Skrondal, A. 2008. Generalized linear mixed effects models. In Longitudinal data analysis: A handbook of modern statistical methods, eds. Fitzmaurice, Garret, Davidian, Marie, Verbeke, Geert, and Molenberghs, Geert, 79106. Boca Raton, FL: Chapman & Hall.
Rehm, Philipp. 2011. Risk inequality and the polarized American electorate. British Journal of Political Science 41: 363–87.
Rehm, Philipp, Hacker, Jacob S., and Schlesinger, Mark. 2012. Insecure alliances: Risk, inequality, and support for the welfare state. American Political Science Review 106: 386406.
Robert, Christan P. 2007. The Bayesian choice: From decision-theoretic foundations to computational implementation. New York: Springer.
Rossi, Peter E., Allenby, Greg M., and Mcculloch, Robert. 2005. Bayesian statistics and marketing. Chichester, UK: Wiley.
Scheve, Kenneth, and Stasavage, David. 2006. Religion and preferences for social insurance. Quarterly Journal of Political Science 1: 255–86.
Shayo, Moses. 2009. A model of social identity with an application to political economy: Nation, class, and redistribution. American Political Science Review 103: 147–74.
Skrondal, Anders, and Rabe-Hesketh, Sophia. 2004. Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. Boca Raton, FL: Chapman & Hall.
Spiegelhalter, D. J., Thomas, A., Best, N., and Gilks, W. R. 1997. BUGS: Bayesian inference using Gibbs sampling manual. Cambridge, UK: Medical Research Council Biostatistics Unit.
Spirling, Arthur, and Quinn, Kevin M. 2010. Identifying intraparty voting blocs in the U.K. House of Commons. Journal of the American Statistical Association 105: 447–57.
Stegmueller, Daniel. 2011. Apples and oranges? The problem of equivalence in comparative research. Political Analysis 19: 471–87.
Varin, Cristiano, and Czado, Claudia. 2010. A mixed autoregressive probit model for ordinal longitudinal data. Biostatistics 11: 127–38.
Vella, F., and Verbeek, Marno. 1998. Whose wages do unions raise? A dynamic model of unionism and wage rate determination for young men. Journal of Applied Econometrics 13: 163–83.
Vermunt, Jeroen. 2004. An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models. Statistica Neerlandica 58: 220–33.
Vermunt, Jeroen, Tran, Bac, and Magidson, Jay. 2008. Latent class models in longitudinal research. In Handbook of longitudinal research, design, measurement, and analysis, ed. Menard, Scott, 373–85. Waltham, MA: Academic Press.
Wawro, G. 2002. Estimating dynamic panel data models in political science. Political Analysis 10: 2548.
Winkelmann, Rainer. 2005. Subjective well-being and the family: Results from an ordered probit model with multiple random effects. Empirical Economics 30: 749–61.
Wlezien, Christopher. 1995. The public as thermostat: Dynamics of preferences for spending. American Journal of Political Science 39: 9811000.
Wooldridge, Jeffrey M. 2002. Econometric analysis of cross section and panel data. Cambridge, MA: MIT Press.———. 2005. Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity. Journal of Applied Econometrics 20: 3954.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
Type Description Title
Supplementary materials

Stegmueller supplementary material

 PDF (210 KB)
210 KB


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed